Ray Optics and Reflection

• Ray optics, also known as geometrical optics, is a simplified model that describes the propagation of light in terms of rays.
• It assumes that light travels in straight lines and bends only when it encounters an interface between two different media.
• Reflection is a phenomenon where light bounces off a surface.
• Reflection obeys two fundamental laws, the law of reflection defines the angles of incidence and reflection.

Law of Reflection

• The incident ray, the reflected ray, and the normal to the surface at the point of incidence all lie in the same plane.
• The angle of incidence (θi) is equal to the angle of reflection (θr).
• The angles are measured with respect to the normal, which is a line perpendicular to the surface at the point where the incident ray strikes.
• These laws hold true for smooth surfaces, such as mirrors.

Types of Reflection

• Specular reflection occurs when light reflects off a smooth surface.
• In specular reflection, parallel incident rays produce parallel reflected rays.
• This type of reflection creates a clear, mirror-like image.
• Diffuse reflection occurs when light reflects off a rough surface.
• In diffuse reflection, parallel incident rays are scattered in different directions upon reflection.
• This type of reflection does not produce a clear image, but it allows us to see the surface from various angles.

Reflection from Plane Mirrors

• A plane mirror is a flat, smooth surface that reflects light specularly.
• The image formed by a plane mirror is virtual, meaning that the light rays do not actually converge at the image location.
• The image appears to be behind the mirror.
• The image is upright, meaning that it has the same orientation as the object.
• The image is laterally inverted, meaning that the left and right sides are reversed.
• The image is the same size as the object.
• The distance from the object to the mirror is equal to the distance from the image to the mirror.

Reflection from Spherical Mirrors

• Spherical mirrors are curved mirrors that have the shape of a portion of a sphere.
• There are two types of spherical mirrors: concave mirrors and convex mirrors.
• Concave mirrors have a reflecting surface that curves inward.
• Convex mirrors have a reflecting surface that curves outward.
• The principal axis of a spherical mirror is a line that passes through the center of curvature (C) and the vertex (V) of the mirror.
• The vertex is the center of the mirror's surface.
• The focal point (F) of a spherical mirror is the point on the principal axis where parallel rays of light converge after reflection from a concave mirror or appear to diverge from after reflection from a convex mirror.
• The focal length (f) of a spherical mirror is the distance from the vertex to the focal point.
• The radius of curvature (R) of a spherical mirror is the distance from the vertex to the center of curvature.
• The focal length is half the radius of curvature: f = R/2.

Image Formation by Concave Mirrors

• The nature of the image formed by a concave mirror depends on the object's position relative to the focal point and the center of curvature.
• If the object is located beyond the center of curvature (u > 2f): The image is real, inverted, and smaller than the object. It is located between the focal point and the center of curvature (f < v < 2f).
• If the object is located at the center of curvature (u = 2f): The image is real, inverted, and the same size as the object. It is located at the center of curvature (v = 2f).
• If the object is located between the center of curvature and the focal point (f < u < 2f): The image is real, inverted, and larger than the object. It is located beyond the center of curvature (v > 2f).
• If the object is located at the focal point (u = f): No image is formed. The reflected rays are parallel.
• If the object is located between the focal point and the mirror (u < f): The image is virtual, upright, and larger than the object. It is located behind the mirror.

Image Formation by Convex Mirrors

• Convex mirrors always produce virtual, upright, and smaller images, regardless of the object's position.
• The image is located behind the mirror, between the focal point and the mirror.
• Convex mirrors have a wider field of view compared to plane or concave mirrors.

Mirror Equation and Magnification

• The mirror equation relates the object distance (u), the image distance (v), and the focal length (f) of a spherical mirror: 1/f = 1/u + 1/v.
• This equation applies to both concave and convex mirrors, but it is important to use the correct sign conventions.
• The magnification (M) of a spherical mirror is defined as the ratio of the image height (hi) to the object height (ho): M = hi/ho = -v/u.
• A positive magnification indicates an upright image, while a negative magnification indicates an inverted image.
• If |M| > 1, the image is larger than the object.
• If |M| < 1, the image is smaller than the object.
• If |M| = 1, the image is the same size as the object.

Sign Conventions

• Object distance (u): Positive if the object is in front of the mirror (real object), negative if the object is behind the mirror (virtual object).
• Image distance (v): Positive if the image is in front of the mirror (real image), negative if the image is behind the mirror (virtual image).
• Focal length (f): Positive for concave mirrors, negative for convex mirrors.
• Radius of curvature (R): Positive for concave mirrors, negative for convex mirrors.
• Image height (hi): Positive for upright images, negative for inverted images.